Question

An electron and a second particle both move in circles perpendicular to a uniformmagnetic field. The mass of the second particle is the same as that of a proton but thecharge of this particle is different from that of a proton. If both particlestakethesameamount of time to go once around their respective circles, determine the charge of thissecond particle. You may use the values:melectron9.1110−31kg,qelectron1.6010−19C, andmproton1.6710−27kg.

Answer 1

The change on the second particle is
`2.93* 10^(-16)\ C`.

Step-by-step explanation:

The period of revolution of the particle in the magnetic field is given by the formula as follows :

`T=(2\pi m)/(Bq)`

It is given that the magnetic field is uniform. The mass of the second particle is the same as that of a proton but thecharge of this particle is different from that of a proton.

`m_s=m_p`

If both particles take the same amount of time to go once around their respective circles. So,

`T_e=T_s\\\\(2\pi m_e)/(Bq_e)=(2\pi m_s)/(Bq_s)\\\\(m_e)/(q_e)=(m_p)/(q_s)\\\\q_s=(m_pq_e)/(m_e)\\\\q_s=(1.67* 10^(-27)* 1.6* 10^(-19))/(9.11* 10^(-31))\\\\q_s=2.93* 10^(-16)\ C`

So, the change on the second particle is
`2.93* 10^(-16)\ C`.